Same issue. Printful support asked me to whitelist a few IP addresses. Did that using cPanel with my provider Bluehost. No change, still 406.
btw on Bluehost at least I can look at log files. Here is what I see:
[client 216.244.66.245:0] [client 216.244.66.245] ModSecurity: Access denied with code 406 (phase 1). Pattern match "NetcraftSurveyAgent|MJ12bot|(?i:BUbiNG)|D(?i:otbot)|
Also, found this summary. Does this mean we need to upgrade to at least a VPS?